Geszetsy, Fritz and Mitrea, Marius and Zinchenko, Maxim (2010) On Dirichlet-to-Neumann Maps, Nonlocal Interactions, and Some Applications to Fredholm Determinants. Few-Body Systems, 47 (1-2). pp. 49-64. ISSN 0177-7963 http://resolver.caltech.edu/CaltechAUTHORS:20100201-115046861
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We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrödinger operators describing nonlocal interactions in L^2 (Ω; d^(n)x), where Ω ⊂ R^n, n ∈ N, n ≥ 2,are open sets with a compact, nonempty boundary ∂Ω satisfying certain regularity conditions. As an application we describe a reduction of a certain ratio of Fredholm perturbation determinants associated with operators in L^2 (Ω; d^(n)x) to Fredholm perturbation determinants associated with operators in L^2(∂Ω; d^(n-1)σ), n ∈ N, n ≥ 2 . This leads to an extension of a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with a Schrödinger operator on the half-line (0, ∞), in the case of local interactions, to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation.
|Additional Information:||© 2010 Springer. Received: 17 May 2009; accepted: 15 July 2009; published online: 8 August 2009. Dedicated with great pleasure to Willi Plessas on the occasion of his 60th birthday. Based upon work partially supported by the US National Science Foundation under Grant Nos. DMS-0400639 and FRG-0456306.|
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|Deposited By:||Jason Perez|
|Deposited On:||01 Feb 2010 23:54|
|Last Modified:||26 Dec 2012 11:44|
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